Non-generic unramified representations in metaplectic covering groups

David Ginzburg*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let G(r) denote the metaplectic covering group of the linear algebraic group G. In this paper we study conditions on unramified representations of the group G(r) not to have a nonzero Whittaker function. We state a general Conjecture about the possible unramified characters χ such that the unramified subrepresentation of IndB(r)G(r)XδB1/2 will have no nonzero Whittaker function. We prove this Conjecture for the groups GLn(r) with r ≥ n − 1, and for the exceptional groups G2(r) when r ≠ 2.

Original languageEnglish
Pages (from-to)447-474
Number of pages28
JournalIsrael Journal of Mathematics
Volume226
Issue number1
DOIs
StatePublished - 1 Jun 2018

Funding

FundersFunder number
Israel Science Foundation259/14

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